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/* ----------------------------------------------------------------------- *

 * This file is part of GEL, http://www.imm.dtu.dk/GEL

 * Copyright (C) the authors and DTU Informatics

 * For license and list of authors, see ../../doc/intro.pdf

 * ----------------------------------------------------------------------- */

#include <iostream>

#include "QEM.h"

#include "LinAlg/LapackFunc.h"

using namespace LinAlg;

using namespace CGLA;

using namespace std;

namespace Geometry

{

	Vec3d QEM::opt_pos(double sv_thresh, const CGLA::Vec3d& p0) const

	{

        CMatrix U,S,V;

        SVD(A,U,S,V);

        CMatrix Sp(3,3,0.0);

        double s00 = S.get(0,0);

        double limit = sv_thresh * s00;

        Sp.set(0,0,1.0/s00);

        Vec3d diff(0.0);

        for(int i=1;i<3;++i)

        {

            double sii = S.get(i,i);

            if(sii < limit)

            {

                Sp.set(i,i,0.0);

                Vec3d vi(V.get(0,i), V.get(1,i), V.get(2,i));

                diff += vi*dot(vi, p0);

            }

            else

                Sp.set(i,i,1.0/sii);

        }

        CMatrix Ap = V * Sp * U.Transposed();

        CVector x(3);

        x = Ap * CVector(b*0.5);

        return diff-Vec3d(x[0],x[1],x[2]);

	}

}